The present invention concerns the field of computer aided design and simulation. In this field three-dimensional (3-D) structural finite element analysis is often used to calculate or simulate various mechanical properties of components during all phases of the design process. In particular, the present invention is concerned with an early step of finite element analysis, namely the generation of three-dimensional meshes for a given structure to be analyzed.
In spite of increasing computing power, the generation of three-dimensional meshes for three-dimensional structural finite element calculations can be a very time-consuming task. This is especially true if hexahedral elements are to be used in the mesh. In the past, several proposals have been made ranging from modular building blocks (see S. Pissanetzky, xe2x80x9cKUBIK: an automatic three-dimensional finite element mesh generatorxe2x80x9d, Int. J. Numer. Meth. Engng., 17, 255-269, 1981) to finite octree techniques (see M. S. Shephard and M. K. Georges, xe2x80x9cAutomatic three-dimensional mesh generation by the finite octree techniquexe2x80x9d, Int. J. Numer. Meth. Engng., 32, 709-749, 1991), midpoint division (see T. S. Li, R. M. McKeag and C. G. Armstrong, xe2x80x9cHexahedral meshing using midpoint subdivision and integer programmingxe2x80x9d, Comput. Methods Appl. Mech. Engng., 124, 171-193, 1995) and mesh projection near the free boundary (see R. Schneiders, xe2x80x9cA grid-based algorithm for the generation of hexahedral element meshesxe2x80x9d, Engineering with Computers, 12, 168-177, 1996). An overview of these and other known techniques is given in the xe2x80x9cHandbook of Grid Generationxe2x80x9d, edited by J. F. Thompson, B. K. Soni and N. P. Weatherill, CRC Press London, 1998. However, in spite of all these attempts, the ultimate goal of a fully automatic tool to create a purely hexahedral mesh containing a reasonable number of elements for an arbitrary structure still has not been reached.
The present invention has the objective of fully or at least partially achieving this goal. In other words, the object of the present invention is to provide a method for generating a three-dimensional, preferably hexahedral, mesh for a structure to be subjected to three-dimensional structural finite element analysis, wherein said method is automated fully or at least to a substantial extent, and wherein the generated three-dimensional mesh has good properties for the subsequent finite element calculations. Preferably, the generated mesh should on the one hand be fine enough to allow accurate finite element calculations and on the other hand have as few elements as possible to reduce the required amount of computation. This balance is normally hard to achieve and often requires some manual interaction.
The invention can be practised performing the described processes in different order or in an interleaved or semi-parallel or parallel fashion.
The present invention is based on the fundamental idea to use a cutting procedure that has originally been developed for automatic crack propagation calculations for the generation of a three-dimensional mesh. A description of this cutting procedure in the context of crack propagation calculations can be found in two articles by the present inventor titled xe2x80x9cAutomatic 3-D mode I crack propagation calculations with finite elementsxe2x80x9d (published in Int. J. Numer. Meth. Engng., 41, 739-757, 1998) and xe2x80x9cCutting of a 3-D finite element mesh for automatic mode I crack propagation calculationsxe2x80x9d (published in Int. J. Numer. Meth. Engng., 42, 749-772, 1998). The disclosure of these two articles is expressly incorporated by reference into the present specification.
The process in accordance with the present invention is to encompass the structure by a master mesh and to cut this master mesh along the external boundaries of the structure. The master mesh preferably is a regular 20-node brick mesh, and the surface of the structure, which does not have to be connected, preferably is described by a triangular mesh.
Using this basic scheme, a three-dimensional mesh suitable for three-dimensional finite element analysis can be generated in a fully or partially automatic fashion. Experiments have shown that finite element calculations using meshes generated by the present invention yield a level of accuracy that is similar to that obtained using a prior art mesh generator requiring a large amount of human interaction and human effort.
In exemplary embodiments of the invention, the three-dimensional mesh is a hexahedral mesh, in particular a mesh having 20-node elements. However, the basic idea of the invention as outlined above is applicable to other mesh topologies as well.
In accordance with the invention, one may use cutting and/or remeshing steps for processing the elements of the master mesh that are intersected by the triangulation. For example, it is possible to cut the elements in order to obtain cut elements having a so-called xe2x80x98simple topologyxe2x80x99. These cut elements may then be subjected to remeshing to generate 20-node brick elements. The remeshing sub-step may also ensure further desirable properties of the mesh elements generated by the method. In some embodiments the elements resulting from the remeshing sub-step are further optimized, for example by a smoothing operation.
An exemplary embodiment of the invention starts with the step of generating a suitable master mesh, based on the triangulation of the structure""s surface. Then, the master mesh elements which are intersected by the triangulation are determined. A 20-node brick element can be intersected in different ways leading to several cutting topologies of which seven are called simple. All other topologies are reduced to these simple ones by appropriate cutting techniques. For each of the simple topologies a remeshing scheme is applied, yielding new 20-node brick elements only. Application of these schemes to the cut elements leads to a fine 20-node element mesh on both sides of the triangulation. Finally, the elements external to the body are discarded.
In some embodiments the newly generated elements are connected to the underlying elements by multiple point constraints (MPCs), or the fine structure is continued into the deeper element layers. Pursuing the latter approach till exhaustion, a pure 20-node brick element mesh may also be obtained.